Orateur
Description
In this joint project with Arno Siri-Jégousse, we introduce a novel research program connecting the fields of mathematical population genetics and self-similar (SS) Markov processes in infinite dimensions. Specifically, we propose a shift in focus from the prevalent paradigm based on the branching property as a tool to analyze the structure of population models, to one based on the self-similarity property. By extending the well-known Lamperti transformation for SS Markov processes to the Banach-valued case, we generalized the celebrated work of Birkner et al. (2005) in population genetics. They describe the genealogies of populations modeled as a measure-valued alpha-stable branching process in terms of the subfamily of Beta coalescents. We describe the genealogies of SS populations whose total size evolves as any positive SS Markov process, in terms of general Lambda coalescents. Along the way we uncover a new duality structure between measure-valued processes on the one hand, and a pair composed of a Lambda-coalescent and a Lévy process on the other. This extends the well-known duality relation between Lambda Fleming-Viot processes and Lambda coalescents of Bertoin and Le Gall (2003).
